- Elliptic curves, L-functions, and the Birch Swinnerton-Dyer
conjecture.

- Modular forms.

- Arithmetic of modular curves.

- Shimura curves and the theory of Cerednik-Drinfeld.

- Iwasawa theory and p-adic L-functions.

- Galois representations attached to modular forms and Fermat's Last Theorem.

To give you an idea of the kind of topics we might cover, here is

- Sept 16:
**Ignazio Longhi**, Introduction to p-adic numbers. - Sept 23:
**Ignazio Longhi**, Introduction to p-adic numbers, cont'd. - Sept 30:
**Malcolm Harper**, The Euclidean algorithm in number rings. - Oct 7:
**Jack Fearnley**, Introduction to elliptic curves. - Oct 21:
**Nicolas Arsenault**, Class groups of GL(2,p)-extensions. - Oct 28:
**Lassina Dembele**, The Hasse-Minkowski theorem. - Nov. 4:
**Jessica Bridson**, Units in real quadratic fields. - Nov. 11:
**Yu-Ru Liu**, Cubic reciprocity. - Nov. 18:
**Francesco Sica**, Riemann's Memoir. - Nov. 25:
**Wei-Dong Tian**, The Kronecker-Weber theorem - Dec. 2:
**Dominic Lemelin**, The proof of Fermat's Last Theorem (Overview) - Dec. 9:
**Dominic Lemelin**, The proof of Fermat's Last Theorem (Cont'd)

- Jan. 22:
**Jack Fearnley**, Curves of genus 1 and Weierstrass equations - Jan. 29:
**Dominic Lemelin**, Elliptic curves over C - Feb. 5:
**Ignazio Longhi**, Tate curves - Feb. 12:
**Steve Thiboutot**, Galois representations attached to elliptic curves: an introduction. - Feb. 19:
**Nicolas Arsenault**, The Weil Pairing. - Feb. 26:
**WEEK OFF** - March 5:
**Odette Barutciski**, Rational torsion points on elliptic curves. - March 12:
**Francesco Sica**, Hecke L-functions. - March 19:
**Lassina Dembele**, Local-global principles for curves of genus one. - March 26:
**Dominic Lemelin**, Elliptic curves with complex multiplication. - April 2:
**Ignazio Longhi**, Class field theory for function fields of curves over finite fields - April 9:
**Nicolas Arsenault**, The Chebotarev density theorem. - April 16:
**TBA**, TBA - April 23:
**TBA**, TBA - April 30:
**Yu-Ru Liu**, The Hasse principle for certain non-homogenous ternary equations. - Coming attraction:
**Steve Thiboutot**, Elliptic curves, Galois representations and the equation x^2+y^3=z^5.